It is known that the hypergeometric function ${}_2F_1(a, b, c; x)$ defined by the series $$\sum_{n=0}^\infty \frac{a(a+1)\cdots (a+n-1)\cdot b(b+1)\cdots (b+n-1)}{c(c+1)\cdots (c+n-1) n!}x^n$$ behaves like $(1-x)^\alpha$ near $x=1$. I am wondering if there is a formula for the $\alpha$ in terms of the constants $a,b$ and $c$. Or, if there exists a criterion determining if $\alpha$ is an integer.

It would be nice if a reference is provided.